Opacity

Opacity is the state of being impenetrable to light. An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through).

When light strikes an interface between two substances, some of the light is reflected, some is absorbed, and the rest is transmitted (also see refraction). An opaque substance transmits very little light, and therefore reflects or absorbs most of it. Both mirrors and jet are opaque. Opacity depends on the frequency of the light being considered. For instance, some kinds of glass, while completely transparent in the visual range, are largely opaque to ultraviolet light. More extreme frequency-dependence is visible in the absorption lines of cold gases. In general, a material tends to emit light in the same proportions as it absorbs it; this is the reason for the equivalence of absorption and emission lines.

Numerical definition

While many materials are so opaque (steel in visible light having near-infinite opacity), and others so transparent (air in visible light having near-zero opacity), that opacity often seems to be a boolean property, others are "somewhat" opaque. Opacity is then in general a static variable: $\kappa _{\nu }$, where the $\nu$ indicates the continuum in question. It has units of reverse length, and is also called the absorption coefficient (see also the opposite extinction coefficient). It gives the proportional rate of absorption (or extinction or how much light intensity is lost for each metre) along a ray of light: ${\partial I_{\nu } \over \partial x}=-I_{\nu }\kappa _{\nu }$. The mean free path is then $1/\kappa _{\nu }$. The notation $\kappa _{\lambda }$ is also used to discuss the physically equivalent description of opacity as a function of wavelength. The opacity of a material, and of a gas in particular, often depends on its temperature and density.

In astronomy and planetary imaging fields, tau, the optical depth, defines the opacity: zero indicates transparent and higher numbers indicate more and more opaque in an inverse exponential fashion, for example a tau of 1 indicates 36 percent of the light passes (e^-1 = 0.36), and a Tau of 5 indicates less than 1 percent passes (e ^-5 = 0.0067).

Opaque Content

An opaque context is a linguistic context in which it is not possible to substitute co-referential terms while guaranteeing the preservation of semantic values.

The term is used in philosophical theories of reference, and is to be contrasted with "transparent context". For example:

Opacity: "Mary knows that Cicero is a great orator" is referentially opaque; although Cicero was also called Tully, we can't simply substitute "Tully" for "Cicero" in this context ("Mary knows that Tully is a great orator"), for Mary might not know that the names 'Tully' and 'Cicero' refer to one and the same thing. Of course, if Mary does know that Cicero is a great orator, then there is a sense in which Mary knows that Tully is a great orator, even if she does not know that 'Tully' and 'Cicero' corefer. It is the sense forced on us by direct theories of reference of proper names, i.e., those that maintain that the meaning of proper names just are their referents.

Transparency: "Cicero was a Roman orator" is referentially transparent; there is no problem substituting "Tully" here: "Tully was a Roman orator". Well, this is an oversimplified account as it may not hold in all circumstances, e.g., when, even though 'Tully' and 'Cicero' are grammatically proper names, their meanings are in part dependent on something other than their referents. This occurs, e.g., when someone has two separate personae that are referred to separately by two distinct proper names, and that, although referring to the same person, do so in significantly different ways that their substitutions into what are usually taken to be transparent contexts results in sentences with different truth values. For example, 'Clark Kent wooed the ladies', or 'Clark Kent was a great hero' are generally taken to be false even though they are true when 'Superman' is substituted for 'Clark Kent' in each.